What happens when two triggered abilities from different players trigger at the same time?

When multiple triggered abilities trigger simultaneously, they are placed on the stack one at a time following a specific order defined by CR 603.3b. First, the Active Player (AP) — the player whose turn it is — chooses the order to put all of their own triggered abilities on the stack. Then, the Non-Active Player (NAP) chooses the order to put all of their own triggered abilities on the stack on top of those.

Because the NAP's triggers are placed on the stack last, they will resolve first. This is a direct consequence of the stack being last-in, first-out (LIFO). Each player has full control over the relative order of their own triggers, but neither player controls the other's triggers.

After all triggered abilities have been placed on the stack, players receive priority again starting with the Active Player (CR 117.3b), and the game proceeds normally — players may respond before any trigger resolves.

Example: It's your turn (you are AP). Your Purphoros, God of the Forge triggers and your opponent's Ob Nixilis, the Adversary trigger both trigger at the same time when a creature enters the battlefield. You put Purphoros's trigger on the stack first, then your opponent puts Ob Nixilis's trigger on top. Ob Nixilis's trigger resolves first, then Purphoros's trigger resolves.

If one player controls triggers from multiple sources simultaneously, they choose the order freely among their own triggers (CR 603.3b). Neither player may interfere with the other's ordering decisions.